A side Note: My league is not representative of my skill level. I haven't had time to play a league game in two weeks and I am far above a gold level of skill. The information below is solid and I'm sure many diamond leaguers will concur.
Step 1: The Foundation (Unit Control and Base Management)
Starcraft 2 is a strategy game with three very distinct races each varying in their buildings and unit abilities. While each race has comparable units (at least statistically) with the other two races, the units are also diverse enough in application that they make each of the three races very distinct in how they play and feel. Such diversity has lead to an almost overwhelming discussion on the internet of strategies and tactics as the pieces of this three way real time speed chess game are much more adaptable than the pieces in chess.
Many people enjoy the chess like strategy involved in the game. However, the speed and precision necessary tend to make the game more akin to an extended and more complex speed chess game than a normal game of strategy chess where players can take their time to think about moves. The game is much more than who can outwit their opponent with a better strategy and adds the element of who can control their units better into the mix. In a game of chess the ability to physically move your pieces around the board matters little, however, in Starcraft 2 it is painfully critical necessity and takes practice to do well. In order to use their strategies effectively players must not only have a solid understanding of the basic strategies involved including unit strengths, weaknesses, build orders and proper placement, but they must also be able to control their units effectively, precisely and quickly. Having a great strategy will get you no where if it takes you far too long to execute that strategy and you spend the majority of your thought process on what keys to hit and what units to build. Think of playing a timed game of chess using only your mouth to move the pieces, your going to have a hard time even though you may have a perfect strategy. It's time to start using your hands!
Taking the above analogies and insight into consideration it is my opinion that the best place for a new player to start learning is how to properly control their units and base quickly, efficiently and with as little thought process as necessary. This control of units and base is a large part of what many players refer to as macro (short for macromanagement).
So how do I become better at controlling my units and my base you may be asking? Well the best way is to become familiar and comfortable with the game. The more you play the more the controls will feel natural to you and the easier the management of your base and units will be. But it is important to develop some good habits from the get go that will not only improve the outcome but the speed at which you learn these skills.
Every unit, action and building in the game has an associated keyboard shortcut (also called a hotkey) which if used properly will be far more efficient and faster than using your mouse to click the control box. If you hover your mouse over the lower right control box where (if for instance you have a barracks selected it will show you the units you can build) units and building are highlighter you will notice the hotkey for that unit will be displayed. There are also many webpages with the hotkeys displayed in a neat little list (use google). Hitting that hotkey on your keyboard will allow the unit to be constructed and when building large amounts of units will be much more efficient than your mouse. In order to get better at this you will have to force yourself to do it when you first start practicing. Force yourself to use hot keys for every game you play, do not use the mouse to build anything! Don't be discouraged if at first your speed seems to slow down and you feel that your doing worse. As you get more comfortable your speed will increase and will soon quickly surpass the speed you had when you were clicking everything.
The second step is to memorize what these hotkeys are and try to play games without even looking at the lower right box. Try and recall from memory what keys you have to press to build a factory or star port. One way that will make memorizing the hotkeys much easier is to switch your control profile over to GRID. You can go into the game option under keybindings and switch to the GRID system which will move all your hotkeys to the upper left part of your keyboard and they will be rather familiar even while switching between the various races.
If you have never used hotkeys before I highly recommend that you start with GRID and never look back. If however you are already used to standard then I would still highly recommend switching over to GRID anyways and just getting used to the new layout as I feel that it is far more efficient than the standard layout. However, keyboard layout is very much a personal choice and if you are pulling 200 APM (Actions per minute) with standard layout then why switch? (Because once mastered you may be able to start pulling 300 APM :)
The key to mastering hotkeys is to focus on only Hotkeys right now. Don't worry about build orders, strategies, control groups or anything else at all. Who cares if you get owned while you work on hotkeys! If you try and learn multiple things at once you will learn all of them slower overall and it will make learning them all the more challenging and things will seem overwhelming leading to frustration which is one of the hugest barriers to learning. You will know you have mastered hotkeys when you can build any building, unit or upgrade in the game as instantly as you can think the name of what you want to build. You should be able to think barracks and immediately have a green silhouetted barracks hovering underneath your mouse ready for placement.